Let $m$ and $n$ be two positive integers between $2$ and $99$, inclusive. Mr. $S$ knows their sum, and Mr. $P$ knows their product. Following are their conversations:

• Mr. $S$: I am certain that you don't know these two numbers individually. But I don't know them either.
• Mr. $P$: Yes, I didn't know. But I know them now.
• Mr. $S$: If this is the case, I know them now too.

What are the two numbers?